Can a neural network be used to detect sine waves?
Is this a task suited for a neural network 


Yes. You have choices in fact:


A fully-connected network would be simplest architecture, and would work if you gave it some time window of samples (e.g. every 0.5 seconds or every 50 samples) and supervised training data - sets of samples with sensor readings and the ground truth value of whether the motor was on or not.
A 1D convolutional neural network would likely be most efficient and robust to train, and would take the same inputs and outputs as the fully-connected network.
A recurrent neural network would be tricker to train, but a nicer design as you could feed it samples one at a time. The input would be the current sample, and output the probability that the motor was on. When training this, you would also want to provide it transitions between the motor being on and off. The nice feature about this is that it should give you quick feedback about whether the motor was on or off - with the caveat that it may be more likely to trigger intermittent false positives, so a little extra post-processing might be required.


All of the above require you to collect training data, ideally in situations identical to planned use of the detector. So if the motor is mounted somewhere that could experience other vibrations, a few of those kind of scenarios should be simulated with motor both on and off.


  and if so, would it be less efficient than other means of detection?


In terms of computing power and effort on your part, you may find that an off-the-shelf Fast Fourier Transform (FFT) library function with a simple threshold at your target frequency will make a robust and simple detector, with no need for a neural network.

Typically for specific frequency detection you would take a window of samples, adjust them (using e.g. Hamming window) to reduce edge effects which would appear as frequencies in the conversion, and then run FFT. This combination is so common that you may find it already combined in the FFT library. For more on this, you would want to ask in Signal Processing Stack Exchange, where use of FFT is well understood.

If the environment is noisy or the target frequency can drift (making it hard to set a simple threshold) then you could also combine FFT with a neural network. This combination can solve much more complicated signal detection, and is used in speech processing for instance.


  sampled at 100Hz - it is possible to increase the sample rate to 200Hz or 400Hz at max


For reliably detecting a 50Hz signal, I would say that 200Hz sample rate is minimum. The theorectical minimum is 100Hz (i.e. twice the signal frequency) but may give you problems with noise and the possibility that your sample points just happen to fall on low amplitude parts of the oscillations, making it look like the motor is off even when it is on.